Triangle A’ B’ C’ is the image of triangle A B C under a rotation about the origin, (0,0)

Which equation represents the equation of the parabola with focus (-3 3) and directrix y=7?

Artemon [7]

Answer:

The equation $y=\frac{-x^2-6x+31}{8}$ represents the equation of the parabola with focus (-3, 3) and directrix y = 7.

Step-by-step explanation:

To find the equation of the parabola with focus (-3, 3) and directrix y = 7. We start by assuming a general point on the parabola (x, y).

Using the distance formula $d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }$ , we find that the distance between (x, y) is

$\sqrt{(x+3)^2+(y-3)^2}$

and the distance between (x, y) and the directrix y = 7 is

$\sqrt{(y-7)^2}$ .

On the parabola, these distances are equal so, we solve for y:

$\sqrt{(x+3)^2+(y-3)^2}=\sqrt{(y-7)^2}\\\\\left(\sqrt{\left(x+3\right)^2+\left(y-3\right)^2}\right)^2=\left(\sqrt{\left(y-7\right)^2}\right)^2\\\\x^2+6x+y^2+18-6y=\left(y-7\right)^2\\\\x^2+6x+y^2+18-6y=y^2-14y+49\\\\y=\frac{-x^2-6x+31}{8}$

6 0

4 years ago

If a = 7 and b = 11, what is the measure of ∠B? (round to the nearest tenth of a degree)

Naddik [55]

Answer:

57.5 degrees

Step-by-step explanation:

Assuming this is a triangle

a is adjacent is ∠B

b is opposite of ∠B

Use the inverse tangent equation: $tan^{-1} (11/7)$

This equals to 57.52880771

3 0

3 years ago

How do you solve -5y-6y=-22

Wewaii [24]

-5y-6y is -11y=-22 so y=2

5 0

4 years ago

70 POINTS Given the function, f (x) = 1/x-1 - 5 , choose the correct transformation.

matrenka [14]

Answer:

right 1, down 5

Step-by-step explanation:

We are given function as

$f(x)=\frac{1}{x-1}-5$

Firstly, we will find parent function

$f(x)=\frac{1}{x}$

We can see that in place of x , we have x-1

so, it is shifted right side by 1 unit

and 5 is subtracted from y-value

so, it is shifted downward by 5 units

right 1, down 5.........Answer

5 0

3 years ago

Read 2 more answers

A simple random sample from a population with a normal distribution of 98 body temperatures has x =98.90 °F and s =0.68°F. Const

Ludmilka [50]

Answer:

$0.609 \leq \sigma \leq 0.772$

And the best conclusion would be:

D. This conclusion is safe because 1.40 °F is outside the confidence interval.

Step-by-step explanation:

1) Data given and notation

s=0.68 represent the sample standard deviation

$\bar x =98.90$ represent the sample mean

n=98 the sample size

Confidence=90% or 0.90

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population mean or variance lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

The Chi Square distribution is the distribution of the sum of squared standard normal deviates .

2) Calculating the confidence interval

The confidence interval for the population variance is given by the following formula:

$\frac{(n-1)s^2}{\chi^2_{\alpha/2}} \leq \sigma^2 \leq \frac{(n-1)s^2}{\chi^2_{1-\alpha/2}}$

The next step would be calculate the critical values. First we need to calculate the degrees of freedom given by:

$df=n-1=98-1=97$

Since the Confidence is 0.90 or 90%, the value of $\alpha=0.1$ and $\alpha/2 =0.05$ , and we can use excel, a calculator or a table to find the critical values.